Xpressions

a truck weighs 5,400 pounds. An open-wheel race car weighs 1/4 as much. how much does the race car weigh

gtnhenbr [62]

Since 1/4 is equal to 0.25 than you would do 5,400 times 0.25 and get the answer of 13,500.0. So the race car weighs 13,500 pounds.

3 0

3 years ago

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The interior angle of a regular polygon is five times its corresponding exterior angle. Find the

tiny-mole [99]

Answer:

12

Step-by-step explanation:

Regular polygon is one in which each angle and sides is congruent.

Sum of all the exterior angles of any polygon is 360.

Sum of all the interior angles of any polygon is (2n-4)*90

where is n is the no. of sides of polygon.

Let n be the no. of sides of polygon required

Therefore,

Sum of all the interior angles of polygon = (2n-4)*90

since no of sides of polygon is n

therefore, value of each interior angles of the polygon = (2n-4)*90/n (A)

Sum of all the exterior angles of any polygon = 360.

value of each exterior angles of the polygon = 360/n (B)

Given that

The interior angle of a regular polygon is five times its corresponding exterior angle (c)

using the statement A, B and C

(2n-4)*90/n = 5*360/n

1/n is common on both side, hence it gets cancelled.

(2n-4)*90 = 5*360

=> (2n-4) = 5*360 /90 = 20

=> 2n = 20+4 = 24

=> n = 24/2 = 12.

the number of sides of the polygon is 12

6 0

3 years ago

5u exponent 7 - 21u exponent 7 Simply

bagirrra123 [75]

Assuming the given is: 5u^7 - 21u^7
Since both algebraic terms are identical (both are using u^7), we can subtract the coefficients directly, as in: 5 - 21 = -16
Therefore, 5u^7 - 21u^7 = -16u^7

7 0

3 years ago

Find the directional derivative of the function at the given point in the direction of the vector v. G(r, s) = tan−1(rs), (1, 3)

alexandr1967 [171]

The directional derivative of $f$ at the given point in the direction indicated is $\frac{5}{2}$ .

<h3>How to calculate the directional derivative of a multivariate function</h3>

The directional derivative is represented by the following formula:

$\nabla_{\vec v} f = \nabla f (r_{o}, s_{o})\cdot \vec v$ (1)

Where:

$\nabla f (r_{o}, s_{o})$ - Gradient evaluated at the point $(r_{o}, s_{o})$ .
$\vec v$ - Directional vector.

The gradient of $f$ is calculated below:

$\nabla f (r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{\partial f}{\partial r}(r_{o},s_{o}) \\\frac{\partial f}{\partial s}(r_{o},s_{o}) \end{array}\right]$ (2)

Where $\frac{\partial f}{\partial r}$ and $\frac{\partial f}{\partial s}$ are the partial derivatives with respect to $r$ and $s$ , respectively.

If we know that $(r_{o}, s_{o}) = (1, 3)$ , then the gradient is:

$\nabla f(r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{s}{1+r^{2}\cdot s^{2}} \\\frac{r}{1+r^{2}\cdot s^{2}}\end{array}\right]$

$\nabla f (r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{3}{1+1^{2}\cdot 3^{2}} \\\frac{1}{1+1^{2}\cdot 3^{2}} \end{array}\right]$

$\nabla f (r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{3}{10} \\\frac{1}{10} \end{array}\right]$

If we know that $\vec v = 5\,\hat{i} + 10\,\hat{j}$ , then the directional derivative is:

$\nabla_{\vec v} f = \left[\begin{array}{cc}\frac{3}{10} \\\frac{1}{10} \end{array}\right] \cdot \left[\begin{array}{cc}5\\10\end{array}\right]$

$\nabla _{\vec v} f (r_{o}, s_{o}) = \frac{5}{2}$

The directional derivative of $f$ at the given point in the direction indicated is $\frac{5}{2}$ . $\blacksquare$

To learn more on directional derivative, we kindly invite to check this verified question: brainly.com/question/9964491

3 0

2 years ago

Need help figuring out this answer.

zmey [24]

Answer:

Volume = 184.8 cm³

Step-by-step explanation:

$Volume of pyramid=\frac{Area of the base*height}{3}$

Area = 44 cm²

Height = 12.6 cm

Put values

$Volume of pyramid=\frac{44*12.6}{3}$

= $\frac{554.4}{3}$

= 184.8cm³

8 0

3 years ago

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