If 4 men in 5 days eat 7 pounds of bread how much will be sufficient for 16 men in 15 days ?

What is the surface area of a prism whose base is each of area 16 m² and who's literal surface area of 64 m²

boyakko [2]

Check the picture below

so you have the lateral area.. just add the area of the bases then, to get the total surface area of the rectangular prism

8 0

3 years ago

Find the equation of the tangent line to the curve (a lemniscate)

olya-2409 [2.1K]

Answer:

$m=\frac{9}{13}$ and $b=\frac{40}{13}$

Step-by-step explanation:

The equation of curve is

$2(x^2+y^2)^2=25(x^2-y^2)$

We need to find the equation of the tangent line to the curve at the point (-3, 1).

Differentiate with respect to x.

$2[2(x^2+y^2)\frac{d}{dx}(x^2+y^2)]=25(2x-2y\frac{dy}{dx})$

$4(x^2+y^2)(2x+2y\frac{dy}{dx})=25(2x-2y\frac{dy}{dx})$

The point of tangency is (-3,1). It means the slope of tangent is $\frac{dy}{dx}_{(-3,1)}$ .

Substitute x=-3 and y=1 in the above equation.

$4((-3)^2+(1)^2)(2(-3)+2(1)\frac{dy}{dx})=25(2(-3)-2(1)\frac{dy}{dx})$

$40(-6+2\frac{dy}{dx})=25(-6-2\frac{dy}{dx})$

$-240+80\frac{dy}{dx})=-150-50\frac{dy}{dx}$

$80\frac{dy}{dx}+50\frac{dy}{dx}=-150+240$

$130\frac{dy}{dx}=90$

Divide both sides by 130.

$\frac{dy}{dx}=\frac{9}{13}$

If a line passes through a points $(x_1,y_1)$ with slope m, then the point slope form of the line is

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

The slope of tangent line is $\frac{9}{13}$ and it passes through the point (-3,1). So, the equation of tangent is

$y-1=\frac{9}{13}(x-(-3))$

$y-1=\frac{9}{13}(x)+\frac{27}{13}$

Add 1 on both sides.

$y=\frac{9}{13}(x)+\frac{27}{13}+1$

$y=\frac{9}{13}(x)+\frac{40}{13}$

Therefore, $m=\frac{9}{13}$ and $b=\frac{40}{13}$ .

5 0

2 years ago

During gym class, Lenny, Lonnie, and Lainey measure the length of their long jumps. Lenny’s jump is ⅔ times the length of Lainey

Svetllana [295]

Answer: Lonnie’s Jump

Step-by-step explanation:

(They just <em>had</em> to give three names that all started with L.)

Since Lenny's jump is ⅔ times the length of Lainey’s, we can tell that Lenny's jump won't be the longest because it is already smaller than Lainey's.

Since Lenny is now out of the picture, let us look at Lonnie and Lainey. Lonnie’s jump is 1 ⅓ times the length of Lainey’s. Since Lonnie's jump is longer than Laniey's, Lonnie's jump is the longest jump.

3 0

2 years ago

This problem please

miskamm [114]

surface areas:

1. 94 ft

2. 96 cm

volumes:

1. 60 ft

2. 42 cm

3 0

2 years ago

Please help meee, I’m having trouble in math. I solved the answer but got none of these.

tino4ka555 [31]

The answer is C

2.5 + 3.4 = 5.9

So:

5.9 x 10^4

6 0

2 years ago