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2 years ago

Hi hi hi higigigiigjssjjsskkskskwkw

Mathematics

2 answers:

Kay [80]2 years ago

5 0

Answer:

Step-by-step explanation:

hows your day going

dybincka [34]2 years ago

4 0

Answer:

are you ok do u need a friend

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The larger of two numbers is 10 less than twice the smaller number. if the sum of the two numbers is 38, find the tqo nubers

Iteru [2.4K]

Let two number A and B, and A >B

as we know A+10=2B① && A+B =38②

①-② solve that
B=16 so A=22

so, they are 16 and 22

3 0

2 years ago

Find the point (,) on the curve =8 that is closest to the point (3,0). [To do this, first find the distance function between (,)

ELEN [110]

Question:

Find the point (,) on the curve $y = \sqrt x$ that is closest to the point (3,0).

[To do this, first find the distance function between (,) and (3,0) and minimize it.]

Answer:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

Step-by-step explanation:

$y = \sqrt x$ can be represented as: $(x,y)$

Substitute $\sqrt x$ for $y$

$(x,y) = (x,\sqrt x)$

So, next:

Calculate the distance between $(x,\sqrt x)$ and $(3,0)$

Distance is calculated as:

$d = \sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}$

So:

$d = \sqrt{(x-3)^2 + (\sqrt x - 0)^2}$

$d = \sqrt{(x-3)^2 + (\sqrt x)^2}$

Evaluate all exponents

$d = \sqrt{x^2 - 6x +9 + x}$

Rewrite as:

$d = \sqrt{x^2 + x- 6x +9 }$

$d = \sqrt{x^2 - 5x +9 }$

Differentiate using chain rule:

Let

$u = x^2 - 5x +9$

$\frac{du}{dx} = 2x - 5$

So:

$d = \sqrt u$

$d = u^\frac{1}{2}$

$\frac{dd}{du} = \frac{1}{2}u^{-\frac{1}{2}}$

Chain Rule:

$d' = \frac{du}{dx} * \frac{dd}{du}$

$d' = (2x-5) * \frac{1}{2}u^{-\frac{1}{2}}$

$d' = (2x - 5) * \frac{1}{2u^{\frac{1}{2}}}$

$d' = \frac{2x - 5}{2\sqrt u}$

Substitute: $u = x^2 - 5x +9$

$d' = \frac{2x - 5}{2\sqrt{x^2 - 5x + 9}}$

Next, is to minimize (by equating d' to 0)

$\frac{2x - 5}{2\sqrt{x^2 - 5x + 9}} = 0$

Cross Multiply

$2x - 5 = 0$

Solve for x

$2x =5$

$x = \frac{5}{2}$

Substitute $x = \frac{5}{2}$ in $y = \sqrt x$

$y = \sqrt{\frac{5}{2}}$

Split

$y = \frac{\sqrt 5}{\sqrt 2}$

Rationalize

$y = \frac{\sqrt 5}{\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$y = \frac{\sqrt {10}}{\sqrt 4}$

$y = \frac{\sqrt {10}}{2}$

Hence:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

3 0

3 years ago

Which of the following equations has no solution?

daser333 [38]

Answer:

B. 3x+5−4x=−(x+8)

Explanation:

3x+5−4x=−(x+8)

Step 1: Simplify both sides of the equation.

3x+5−4x=−(x+8)

3x+5+−4x=−x+−8

(3x+−4x)+(5)=−x−8

−x+5=−x−8

Step 2: Add x to both sides.

−x+5+x=−x−8+x

5=−8

Step 3: Subtract 5 from both sides.

5−5=−8−5

0=−13

So, there is no solution

Hope this Helps!

8 0

2 years ago

Read 2 more answers

Evaluate the expression 3.14(7)^2

ruslelena [56]

Answer:

153.86

Step-by-step explanation:

3.14(7)^2

3.14 × (7 × 7)

3.14 × 49

153.86

6 0

2 years ago

If a dies is rolled one time, find these probabilities. getting a number less than or equal to 4

trapecia [35]

Hi there!

So let's see, we have a die and need to know the probability of rolling a number less than or equal to 4. Let's list the numbers that are less than or equal to 4: 1, 2, 3, 4. Now, since we know that there are 6 numbers on a die and 4 of them are less than or equal to 4, we can set up a fraction to find the percentage. The fraction would be 4/6 because 4 out of the 6 numbers on the die are less than or equal to 6. We can simplify 4/6 to 2/3 as well. To find the percentage, all we need to do is divide the numerator by the denominator. This leaves us with approximately 66.66%.

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!

5 0

2 years ago