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2 years ago

--2m + 4n2 for m = -6 and n=-5 Evaluate the expression

Mathematics

1 answer:

Tamiku [17]2 years ago

7 0

Answer: 112

Step-by-step explanation:

Since we were given m and n, we plug them into the expression and solve.

-2(-6)+4(-5)² [exponent]

-2(-6)+4(25) [multiply]

12+100 [add]

112

Now, we know that the value of the expression is 112.

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Jose is very hungry after doing his math homework he agrees to pay for 2/3 of the pizza that he and Charlie ordered the pizza co

Brilliant_brown [7]

$6.20.
2/3=.6666666667
Multiple 9.30 by .6666666667 and you will get the 2/3 cost of the pizza.

6 0

3 years ago

If f(x, y, z) = x sin(yz), (a) find the gradient of f and (b) find the directional derivative of f at (2, 4, 0) in the direction

valentina_108 [34]

Answer:

a) $\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}$ .

b) $Du_{f}(2,4,0) = -\frac{8}{\sqrt{11}}$

Step-by-step explanation:

Given a function $f(x,y,z)$ , this function has the following gradient:

$\nabla f(x,y,z) = f_{x}(x,y,z)\mathbf{i} + f_{y}(x,y,z)\mathbf{j} + f_{z}(x,y,z)\mathbf{k}$ .

(a) find the gradient of f

We have that $f(x,y,z) = x\sin{yz}$ . So

$f_{x}(x,y,z) = \sin{yz}$

$f_{y}(x,y,z) = xz\cos{yz}$

$f_{z}(x,y,z) = xy \cos{yz}$ .

$\nabla f(x,y,z) = f_{x}(x,y,z)\mathbf{i} + f_{y}(x,y,z)\mathbf{j} + f_{z}(x,y,z)\mathbf{k}$ .

$\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}$

(b) find the directional derivative of f at (2, 4, 0) in the direction of v = i + 3j − k.

The directional derivate is the scalar product between the gradient at (2,4,0) and the unit vector of v.

We have that:

$\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}$

$\nabla f(2,4,0) = \sin{0}\mathbf{i} + 0\cos{0}\mathbf{j} + 8 \cos{0}\mathbf{k}$ .

$\nabla f(2,4,0) = 0i+0j+8k=(0,0,8)$

The vector is $v = i + 3j - k = (1,3,-1)$

To use v as an unitary vector, we divide each component of v by the norm of v.

$|v| = \sqrt{1^{2} + 3^{2} + (-1)^{2}} = \sqrt{11}$

$v_{u} = (\frac{1}{\sqrt{11}}, \frac{3}{\sqrt{11}}, \frac{-1}{\sqrt{11}})$

Now, we can calculate the scalar product that is the directional derivative.

$Du_{f}(2,4,0) = (0,0,8).(\frac{1}{\sqrt{11}}, \frac{3}{\sqrt{11}}, \frac{-1}{\sqrt{11}}) = -\frac{8}{\sqrt{11}}$

6 0

3 years ago

A multivitamin tablet contains 10.5 mg of calcium. How much calcium does a bottle of 50 tablets contain? Write your answer in gr

andrew11 [14]

Just do 10.5 × 50 and whatever answer you get label as grams

4 0

3 years ago

Read 2 more answers

Can u guys help me with this problem

netineya [11]

Answer:

$-0.7$ or $-\frac{7}{10}$

Step-by-step explanation:

$-0.75-(-\frac{2}{5})+0.4+(-\frac{3}{4})$

The opposite of $-\frac{2}{5}$ is $\frac{2}{5}$

$-0.75 + \frac{2}{5} +0.4 - \frac{3}{4}$

Convert decimal number −0.75 to fraction $-\frac{75}{100}$ .

Reduce the fraction $-\frac{75}{100}$ to lowest terms by extracting and canceling out 25.

$-\frac{3}{4} + \frac{2}{5}+0.4-\frac{3}{4}$

Least common multiple of 4 and 5 is 20. Convert $-\frac{3}{4}$ and $\frac{2}{5}$ to fractions with denominator 20.

$-\frac{15}{20}+ \frac{8}{20} +0.4 - \frac{3}{4}$

Since $-\frac{15}{20}$ and $\frac{8}{20}$ have the same denominator, add them by adding their numerators.

$\frac{-15 +8}{20} +0.4-\frac{3}{4}$

Add -15 and 8 to get -7

$-\frac{7}{20}+0.4-\frac{3}{4}$

Convert decimal number 0.4 to fraction $\frac{4}{10}$ . Reduce the fraction $\frac{4}{10}$ to lowest terms by extracting and canceling out 2.

$-\frac{7}{20}+\frac{2}{5}-\frac{3}{4}$

Least common multiple of 20 and 5 is 20. Convert $-\frac{7}{20}$ and $\frac{2}{5}$ to fractions with denominator 20.

$-\frac{7}{20}+\frac{8}{20}-\frac{3}{4}$

Since $-\frac{7}{20}$ and $\frac{8}{20}$ have the same denominator, add them by adding their numerators.

$20-7+8-\frac{3}{4}$

Add -7 and 8 to get 1.

$\frac{1}{20}-\frac{3}{4}$

Least common multiple of 20 and 4 is 20. Convert $\frac{1}{20}$ and $\frac{3}{4}$ to fractions with denominator 20.

$\frac{1}{20}-\frac{15}{20}$

Since $\frac{1}{20}$ and $\frac{15}{20}$ have the same denominator, subtract them by subtracting their numerators.

$\frac{1}{20}-15$

Subtract 15 from 1 to get -14.

$20-14$

Reduce the fraction $-\frac{14}{20}$ to lowest terms by extracting and canceling out 2.

$-\frac{7}{10}$ or $-0.7$

Hope this helps! Brainliest would be much appreciated! Have a great day! :)

8 0

2 years ago

A ladder leans against a building that angle of elevation of the latter is 70° the top of the ladder is 25 feet from the ground.

VashaNatasha [74]

Answer:

a. 20.5

Step-by-step explanation:

because this will form a right triangle we can use tan (opposite over adjacent) so an equation we could set up would be tan(70)=25/x

therefore we can just solve the equation which would give us 20.45. so if we round it the answer would be a

3 0

2 years ago

Read 2 more answers