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2 years ago

The sum of d and 67 is equal to f. Let f = 83.

Mathematics

2 answers:

Fynjy0 [20]2 years ago

6 0

F=d+67
83=d+67
83-67=d
16=d

Maslowich2 years ago

5 0

Answer:

d = 16

Step-by-step explanation:

f - 67

83 - 67 = 16

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Please help. with question number 16

ddd [48]

Answer:

12/5

Step-by-step explanation:

All you do is multiply

8 0

3 years ago

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2/3 + y2/3 = 4 (−3 3 , 1)

vovikov84 [41]

Answer with Step-by-step explanation:

We are given that an equation of curve

$x^{\frac{2}{3}}+y^{\frac{2}{3}}=4$

We have to find the equation of tangent line to the given curve at point $(-3\sqrt3,1)$

By using implicit differentiation, differentiate w.r.t x

$\frac{2}{3}x^{-\frac{1}{3}}+\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=0$

Using formula : $\frac{dx^n}{dx}=nx^{n-1}$

$\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=-\frac{2}{3}x^{-\frac{1}{3}}$

$\frac{dy}{dx}=\frac{-\frac{2}{3}x^{-\frac{1}{3}}}{\frac{2}{3}y^{-\frac{1}{3}}}$

$\frac{dy}{dx}=-\frac{x^{-\frac{1}{3}}}{y^{-\frac{1}{3}}}$

Substitute the value x= $-3\sqrt3,y=1$

Then, we get

$\frac{dy}{dx}=-\frac{(-3\sqrt3)^{-\frac{1}{3}}}{1}$

$\frac{dy}{dx}=-(-3^{\frac{3}{2}})^{-\frac{1}{3}}=-\frac{1}{-(3)^{\frac{3}{2}\times \frac{1}{3}}}=\frac{1}{\sqrt3}$

Slope of tangent=m= $\frac{1}{\sqrt3}$

Equation of tangent line with slope m and passing through the point $(x_1,y_1)$ is given by

$y-y_1=m(x-x_1)$

Substitute the values then we get

The equation of tangent line is given by

$y-1=\frac{1}{\sqrt3}(x+3\sqrt3)$

$y-1=\frac{x}{\sqrt3}+3$

$y=\frac{x}{\sqrt3}+3+1$

$y=\frac{x}{\sqrt3}+4$

This is required equation of tangent line to the given curve at given point.

8 0

3 years ago

Which function is linear? Select all that apply.

rjkz [21]

Answer:

C and D

Step-by-step explanation:

I'm guessing the 3 in A and B are exponents, only equations with an highest exponent of 1 is linear

8 0

2 years ago

Read 2 more answers

The county hospital is located at the center of a square whose sides are 3 miles wide. If an accident occurs within this square,

Dmitry_Shevchenko [17]

Answer:

Step-by-step explanation:

The x-coordinate of the accident is a random variable of uniform distribution with range [-1.5,1.5]. The same can be said for the y-coordinate. However, |x| and |y| are also uniform variables with range [0,1.5], since we still have the same probability on every pair of intervals with the same lenght.

Note that |X| and |Y| are independent with each other, therefore E(|x|+|y|) = E(|x|) + E(|y|) = 2*E(|x|). The last equality holds because both x and y are identically distributed, then so are |x| and |y|.

E(|x|) = $\int\limits^{1.5}_0 {\frac{x}{1.5} \, dx = \frac{2}{3}* ((1.5^2)/2 - 0^2/2) = \frac{3}{2}$

Therefore, E(|x| + |y|) = 2 * 3/2 = 3.

I hope that works for you!

4 0

3 years ago

A rectangular mural has dimensions of (x + 10) and (x + 3) feet. If the area of the mural is 60

Crank

Answer:

Dimensions are 12 , 5

Step-by-step explanation:

Area of rectangular mural = length * width

length * width = 60 square feet

(x + 10)(x + 3) = 60

Use FOIL method

x*x + x*3 + 10*x + 10*3 = 60

x² + <u>3x + 10x</u> + 30 = 60 {Combine like terms}

x² +<u> 13x</u> + 30 - 60 = 0

x² + 13x - 30 = 0

Sum = 13

Product = -30

Factors = 15 , -2 (15+ (-2) = 13 ; 15*(-2) = -30)

x² + 15x - 2x - 30 =0 {Rewrite middle terms}

x(x + 15) - 2(x + 15) = 0

(x + 15)(x - 2) =0

x - 2 = 0 {Ignore (x +15) as dimensions wont have a negative value}

x = 2

x + 10 = 2 + 10 = 12

x + 3 = 2 + 3 = 5

Dimensions are 12 , 5

3 0

2 years ago